t = I aThere is a disc and a hoop of equal masses that can be placed on a rotation platform that has a cylinder at the bottom. A string is wrapped around the cylinder at the bottom of the platform. The string passes over a pulley and is attached to a weight. Place the disc on the platform and wind the platform until the weight is located at a fix point near the top of the pulley. Release the platform and record the time it takes for the weight to reach the ground. Repeat using the ring. Noting the radius of the cylinder, find the angular acceleration for each case. Find the ratio of the two values.
The mass of an object is really define as the ratio of the force on the object to the acceleration caused by that force. Similarly, the moment of inertia of an object is the ratio of the torque (in this case it is the force of the weight times the radius of cylinder at which it acts) to the angular acceleration caused by that torque. What is the ratio of the moments of inertia for the disc and cylinder? (If time permits, you may wish to calculate the actual values of each moment of inertia.)
Each member of the group sits on the platform and is handed the bicycle wheel spinning in the vertical plane. Give the subject a small angular velocity. Repeat several times reversing the direction of spin of the wheel and platform. Repeat with the wheel spinning in a horizontal plane. The subject should note the forces and resultant torque necessary to maintain the wheel's orientation. Using top and side view diagrams, show the direction of L, the change in L, and the applied torque t in each case.
One person from your group is seated stationary on the rotation platform. This person is handed a bicycle wheel spinning in a horizontal plane. Note the direction of the angular momentum (L) of the wheel. The person now rotates the wheel axis through 180 degrees. Using diagrams indicate what happens and explain the results using conservation of angular momentum.
Iiwi = IfwfA volunteer member of the group stands on the platform with arms hanging vertically at their side. Try a few gentle spins to be sure the person is center on the platform. Give the subject a small angular velocity ( < 1 rps ) and measure this value by finding the time required for 2 rotations. The subject then quickly raises the arms to a horizontal position and the new time for two rotations is measured. Do not touch the subject during the procedure. There is a double time feature on the stopwatches that will minimize the number of rotations required to do this.
Repeat the procedure with 1 kg masses held in the hands, and a third time using 2 kg masses if the volunteer is strong enough. (It is possible that the rotation with the arms out will be slow enough that measuring the time of one rotation will be sufficent.)
Find the ratio of the rates of rotation for each experiment. Then compare the ratios to one another. Can you identify any trends in the ratio resulting from the addition of the masses?
A cat with its back to the ground can rotate itself 180 degrees while falling in order to land on its feet. It does this with no initial or net angular momentum! Can you explain this? First, use the platform and the bicycle wheel to convince yourself that rotations can be achieved without a net angular momentum.
Seat yourself on the platform and devise a method to achieve a net rotation using your arms and legs. Do not use the friction inherent in the platform by using quick, jerking motions! You may wish to put weights in your hands to increase the effectiveness of arm motions. (A cat has great flexibility that allows for very effective movements.) Describe your method.